Applied Mathematics & Optimization

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Biorthogonal Functions for Complex Exponentials and an Application to the Controllability of the Kawahara Equation Via a Moment Approach
Applied Mathematics & Optimization - - 2023
Ademir F. Pazoto, Marcelo Bernardes Vieira
Điều Kiện Tối Ưu Cần Thiết cho Một Số Vấn Đề Điều Khiển của Các Phương Trình Bậc Hai với Điều Kiện Biên Venttsel Dịch bởi AI
Applied Mathematics & Optimization - Tập 61 - Trang 337-351 - 2009
Yousong Luo
Trong bài báo này, chúng tôi đưa ra một điều kiện tối ưu cần thiết cho một nghiệm tối ưu địa phương của một số bài toán điều khiển. Các bài toán điều khiển tối ưu này được quản lý bởi một bài toán giá trị biên Venttsel nửa tuyến tính của một phương trình elliptic tuyến tính. Kiểm soát được áp dụng cho phương trình trạng thái thông qua biên và một chức năng của điều khiển cùng với nghiệm của phương...... hiện toàn bộ
#tối ưu #điều kiện tối ưu #bài toán điều khiển #phương trình elliptic #điều kiện biên Venttsel
Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms
Applied Mathematics & Optimization - Tập 87 - Trang 1-22 - 2023
Brian Straughan
We present models for convection in a mixture of viscous fluids when the layer is heated from below and simultaneously the pointwise volume concentration of one of the fluids is heavier below. This configuration produces a problem of competitive double diffusion since heating from below promotes instability, but the greater density of fluid below is stabilizing. The fluids are of linear viscous ty...... hiện toàn bộ
A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks
Applied Mathematics & Optimization - Tập 74 - Trang 375-421 - 2015
Dan Goreac, Magdalena Kobylanski, Miguel Martinez
We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networ...... hiện toàn bộ
A topology for Markov controls
Applied Mathematics & Optimization - - 1989
Vivek S. Borkar
Backward Stochastic Differential Equations in Infinite Dimensions with Continuous Driver and Applications
Applied Mathematics & Optimization - Tập 56 - Trang 265-302 - 2007
Marco Fuhrman, Ying Hu
In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.
Sensitivity analysis of optimization problems in Hilbert space with application to optimal control
Applied Mathematics & Optimization - Tập 21 - Trang 1-20 - 1990
Kazimierz Malanowski
A family of optimization problems in a Hilbert space depending on a vector parameter is considered. It is assumed that the problems have locally isolated local solutions. Both these solutions and the associated Lagrange multipliers are assumed to be locally Lipschitz continuous functions of the parameter. Moreover, the assumption of the type of strong second-order sufficient condition is satisfied...... hiện toàn bộ
Optimal Control and Zero-Sum Stochastic Differential Game Problems of Mean-Field Type
Applied Mathematics & Optimization - - 2018
Boualem Djehiche, Said Hamadène
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type.
A Study of Certain Sharp Poincaré Constants as Set Functions of Their Domain
Applied Mathematics & Optimization - - 2023
Jonathan J. Bevan, Jonathan H. B. Deane
AbstractFor bounded, convex sets $$\Omega \subset \mathbb {R}^d$$ Ω ⊂ R d , the sharp Poincaré constant $$C(\Omega )$$ C ( Ω ) , which appears in $$||f-\bar{f}_{_{\Omega }}||_{L^{\infty }(\Omega )} \le C(\Omega )||\nabla f||_{L^{\infty }(\Omega )}$$ | | f - f ¯ Ω | | L ∞ ( Ω ) ≤ C ( Ω ) | | ∇ f | | L ∞ ( Ω ) , is given by $$C(\Omega )=\max _{_{\partial \Omega }}\zeta $$ C ( Ω ) = max ∂ Ω ζ for a specific convex function $$\zeta $$ ζ [Bevan et al. in Proc Am Math Soc 151:1071–1085, 2023 (Theorem 1.1)]. We study $$C(\cdot )$$ C ( · ) as a function on convex sets, in particular on polyhedra, and find that while a geometric characterization of $$C(\Omega )$$ C ( Ω ) for triangles is possible, for other polyhedra the problem of ordering $$\zeta (V_i)$$ ζ ( V i ) , where $$V_i$$ V i are the vertices of $$\Omega $$ Ω , can be formidable. In these cases, we develop estimates of $$C(\Omega )$$ C ( Ω ) from above and below in terms of more tractable quantities. We find, for example, that a good proxy for C(Q) when Q is a planar polygon with vertices $$V_i$$ V i and centroid $$\gamma (Q)$$ γ ( Q ) is the quantity $$D(Q)=\max _{i}|V_i-\gamma (Q)|$$ D ( Q ) = max i | V i - γ ( Q ) | , with an error of up to $$\sim 8\%$$ ∼ 8 % . A numerical study suggests that a similar statement holds for k-gons, this time with a maximal error across all k-gons of $$\sim 13\%$$ ∼ 13 % . We explore the question of whether there is, for each $$\Omega $$ hiện toàn bộ
Existence, uniqueness, and regularity results for the two-body contact problem
Applied Mathematics & Optimization - Tập 15 - Trang 251-277 - 1987
Paolo Boieri, Fabio Gastaldi, David Kinderlehrer
The problem of contact between two elastic bodies is studied under the assumption of nonzero initial gap in the potential contact region. The related variational inequality is stated and existence, uniqueness, and local regularity results are proved for its solution.
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